## Linear Operators, Part 2 |

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Results 1-3 of 47

Page 1220

It is clear that G(S, Z, 11) is a linear manifold in the space 1lI(S, Z, v) of all v-

measurable functions on S and that a set of functions in G(S, Z, v) is

linear ...

It is clear that G(S, Z, 11) is a linear manifold in the space 1lI(S, Z, v) of all v-

measurable functions on S and that a set of functions in G(S, Z, v) is

**linearly****independent**in llI(S, Z, v) if and only if it is**linearly independent**in G(S,Z, v). Thelinear ...

Page 1306

The following table gives the number of

a = 0 square integrable at a or b when .f(}.) ;é 0. There are four possibilities as

shown by the discussion above O Number of

The following table gives the number of

**linearly independent**solutions of (1: -1.)a = 0 square integrable at a or b when .f(}.) ;é 0. There are four possibilities as

shown by the discussion above O Number of

**linearly independent**solutions ...Page 1311

The operator T = T(r) will be an operator obtained from -r by the imposition of a

set, which may be vacuous, of k

0, i = 1, . . ., k; i.e., T is the restriction of T1(r) (cf. Definition 2.8) to the submanifold

...

The operator T = T(r) will be an operator obtained from -r by the imposition of a

set, which may be vacuous, of k

**linearly independent**boundary conditions B,(f) =0, i = 1, . . ., k; i.e., T is the restriction of T1(r) (cf. Definition 2.8) to the submanifold

...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Paoor partial differential operator Pnoor positive preceding lemma Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero